The data set contains 1989 records. The overall descriptive statistics:
## Married Meet credit history guidelines
## No : 678 0 : 171
## Unknown: 3 1 :1816
## Yes :1308 666: 2
##
##
##
## Other obligations as a percent of total income non-Hispanic Black
## Min. : 0.00 No :1792
## 1st Qu.:28.00 Yes: 197
## Median :33.00
## Mean :32.39
## 3rd Qu.:37.00
## Max. :95.00
## Hispanic Male Mortgage loan approved
## No :1878 No : 369 No : 244
## Yes: 111 Unknown: 15 Yes:1745
## Yes :1605
##
##
##
## Loan amount/purchase price Race
## Min. : 2.105 Hispanic : 111
## 1st Qu.: 70.000 non-Hispanic Black: 197
## Median : 80.000 non-Hispanic White:1681
## Mean : 77.064
## 3rd Qu.: 89.894
## Max. :257.143
Descriptive statistics by Race:
## $Hispanic
## MARRIED GDLIN OBRAT MALE APPROVE
## No :31 0 :16 Min. :14.60 No :22 No :26
## Unknown: 1 1 :95 1st Qu.:29.00 Unknown: 2 Yes:85
## Yes :79 666: 0 Median :33.00 Yes :87
## Mean :33.46
## 3rd Qu.:38.45
## Max. :62.00
## LOANPRC RACE
## Min. : 39.39 Hispanic :111
## 1st Qu.: 80.00 non-Hispanic Black: 0
## Median : 89.39 non-Hispanic White: 0
## Mean : 85.17
## 3rd Qu.: 90.42
## Max. :162.63
##
## $`non-Hispanic Black`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 76 0 : 53 Min. : 5.60 No : 51 No : 64
## Unknown: 0 1 :144 1st Qu.:31.00 Unknown: 2 Yes:133
## Yes :121 666: 0 Median :35.00 Yes :144
## Mean :34.94
## 3rd Qu.:38.90
## Max. :63.00
## LOANPRC RACE
## Min. : 28.99 Hispanic : 0
## 1st Qu.: 80.00 non-Hispanic Black:197
## Median : 87.02 non-Hispanic White: 0
## Mean : 83.97
## 3rd Qu.: 90.24
## Max. :255.52
##
## $`non-Hispanic White`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 571 0 : 102 Min. : 0.00 No : 296 No : 154
## Unknown: 2 1 :1577 1st Qu.:27.60 Unknown: 11 Yes:1527
## Yes :1108 666: 2 Median :32.50 Yes :1374
## Mean :32.02
## 3rd Qu.:36.50
## Max. :95.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 0
## 1st Qu.: 68.182 non-Hispanic Black: 0
## Median : 79.888 non-Hispanic White:1681
## Mean : 75.719
## 3rd Qu.: 89.623
## Max. :257.143
Descriptive statistics by Marital Status:
## $No
## MARRIED GDLIN OBRAT MALE APPROVE
## No :678 0 : 64 Min. : 4.00 No :252 No :102
## Unknown: 0 1 :614 1st Qu.:28.00 Unknown: 7 Yes:576
## Yes : 0 666: 0 Median :33.00 Yes :419
## Mean :32.74
## 3rd Qu.:37.00
## Max. :83.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 31
## 1st Qu.: 72.426 non-Hispanic Black: 76
## Median : 80.000 non-Hispanic White:571
## Mean : 77.967
## 3rd Qu.: 89.978
## Max. :162.626
##
## $Unknown
## MARRIED GDLIN OBRAT MALE APPROVE LOANPRC
## No :0 0 :0 Min. :13.0 No :1 No :0 Min. : 86.96
## Unknown:3 1 :3 1st Qu.:23.3 Unknown:0 Yes:3 1st Qu.: 88.62
## Yes :0 666:0 Median :33.6 Yes :2 Median : 90.29
## Mean :27.2 Mean : 98.16
## 3rd Qu.:34.3 3rd Qu.:103.76
## Max. :35.0 Max. :117.24
## RACE
## Hispanic :1
## non-Hispanic Black:0
## non-Hispanic White:2
##
##
##
##
## $Yes
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 0 0 : 107 Min. : 0.00 No : 116 No : 142
## Unknown: 0 1 :1199 1st Qu.:28.00 Unknown: 8 Yes:1166
## Yes :1308 666: 2 Median :33.00 Yes :1184
## Mean :32.22
## 3rd Qu.:37.00
## Max. :95.00
## LOANPRC RACE
## Min. : 8.772 Hispanic : 79
## 1st Qu.: 68.857 non-Hispanic Black: 121
## Median : 80.000 non-Hispanic White:1108
## Mean : 76.547
## 3rd Qu.: 89.866
## Max. :257.143
Descriptive statistics by Gender:
## $No
## MARRIED GDLIN OBRAT MALE APPROVE
## No :252 0 : 31 Min. : 6.99 No :369 No : 50
## Unknown: 1 1 :338 1st Qu.:28.00 Unknown: 0 Yes:319
## Yes :116 666: 0 Median :33.00 Yes : 0
## Mean :32.64
## 3rd Qu.:37.00
## Max. :83.00
## LOANPRC RACE
## Min. : 11.01 Hispanic : 22
## 1st Qu.: 70.83 non-Hispanic Black: 51
## Median : 80.00 non-Hispanic White:296
## Mean : 77.66
## 3rd Qu.: 90.00
## Max. :255.52
##
## $Unknown
## MARRIED GDLIN OBRAT MALE APPROVE
## No :7 0 : 0 Min. :24.00 No : 0 No : 0
## Unknown:0 1 :15 1st Qu.:29.95 Unknown:15 Yes:15
## Yes :8 666: 0 Median :34.50 Yes : 0
## Mean :33.33
## 3rd Qu.:37.65
## Max. :40.30
## LOANPRC RACE
## Min. :39.39 Hispanic : 2
## 1st Qu.:74.93 non-Hispanic Black: 2
## Median :75.42 non-Hispanic White:11
## Mean :75.59
## 3rd Qu.:80.43
## Max. :92.90
##
## $Yes
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 419 0 : 140 Min. : 0.00 No : 0 No : 194
## Unknown: 2 1 :1463 1st Qu.:28.00 Unknown: 0 Yes:1411
## Yes :1184 666: 2 Median :33.00 Yes :1605
## Mean :32.32
## 3rd Qu.:37.00
## Max. :95.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 87
## 1st Qu.: 69.655 non-Hispanic Black: 144
## Median : 80.000 non-Hispanic White:1374
## Mean : 76.942
## 3rd Qu.: 89.881
## Max. :257.143
There are 3 records are missing married (MARRIED) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC | RACE |
|---|---|---|---|---|---|---|---|---|---|
| 356 | Unknown | 1 | 35.0 | No | Yes | Yes | Yes | 86.95652 | Hispanic |
| 759 | Unknown | 1 | 33.6 | No | No | Yes | Yes | 90.28571 | non-Hispanic White |
| 1392 | Unknown | 1 | 13.0 | No | No | No | Yes | 117.24140 | non-Hispanic White |
There are 3 records are missing married (GDLIN) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC | RACE |
|---|---|---|---|---|---|---|---|---|---|
| 881 | Yes | 666 | 35 | No | No | Yes | Yes | 75.82939 | non-Hispanic White |
| 1229 | Yes | 666 | 26 | No | No | Yes | Yes | 100.00000 | non-Hispanic White |
There are 15 records are missing gender (MALE) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC | RACE |
|---|---|---|---|---|---|---|---|---|---|
| 1 | No | 1 | 34.5 | No | No | Unknown | Yes | 75.42373 | non-Hispanic White |
| 127 | No | 1 | 31.6 | No | No | Unknown | Yes | 80.80000 | non-Hispanic White |
| 286 | Yes | 1 | 37.3 | No | No | Unknown | Yes | 80.05337 | non-Hispanic White |
| 452 | Yes | 1 | 40.1 | Yes | No | Unknown | Yes | 75.00000 | non-Hispanic Black |
| 618 | Yes | 1 | 38.5 | No | No | Unknown | Yes | 92.90323 | non-Hispanic White |
| 695 | Yes | 1 | 25.0 | No | No | Unknown | Yes | 64.48276 | non-Hispanic White |
| 762 | Yes | 1 | 27.6 | No | No | Unknown | Yes | 75.55556 | non-Hispanic White |
| 768 | No | 1 | 35.6 | No | No | Unknown | Yes | 64.74397 | non-Hispanic White |
| 833 | Yes | 1 | 24.0 | No | Yes | Unknown | Yes | 79.80769 | Hispanic |
| 979 | No | 1 | 31.7 | No | No | Unknown | Yes | 74.86033 | non-Hispanic White |
| 1040 | No | 1 | 38.0 | Yes | No | Unknown | Yes | 75.38462 | non-Hispanic Black |
| 1070 | Yes | 1 | 40.3 | No | Yes | Unknown | Yes | 39.39394 | Hispanic |
| 1092 | Yes | 1 | 29.7 | No | No | Unknown | Yes | 90.10239 | non-Hispanic White |
| 1613 | No | 1 | 30.2 | No | No | Unknown | Yes | 90.00000 | non-Hispanic White |
| 1924 | No | 1 | 35.8 | No | No | Unknown | Yes | 75.32051 | non-Hispanic White |
## APPROVE
## RACE No Yes
## Hispanic 26 85
## non-Hispanic Black 64 133
## non-Hispanic White 154 1527
## APPROVE
## MARRIED No Yes
## No 102 576
## Unknown 0 3
## Yes 142 1166
## APPROVE
## MALE No Yes
## No 50 319
## Unknown 0 15
## Yes 194 1411
## , , RACE = Hispanic
##
## APPROVE
## MARRIED No Yes
## No 7 24
## Unknown 0 1
## Yes 19 60
##
## , , RACE = non-Hispanic Black
##
## APPROVE
## MARRIED No Yes
## No 27 49
## Unknown 0 0
## Yes 37 84
##
## , , RACE = non-Hispanic White
##
## APPROVE
## MARRIED No Yes
## No 68 503
## Unknown 0 2
## Yes 86 1022
log(p/1-p) = \(b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * MALE + b_6 * LOANPRC + b_7 * MARRIED\)
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.38153 3.71927 -0.03407 -0.81569 -0.90001
## LOANPRC MARRIED1 MALE1
## -0.01681 0.47574 -0.05395
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1961 Residual
## Null Deviance: 1475
## Residual Deviance: 959.4 AIC: 975.4
For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0340739.
For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0168119.
The log odds of loan approval for applicants that meet credit guidelines increases by 3.719269.
The log odds of loan approval for married applicants increases by 0.4757419.
The log odds of loan approval for Black applicants decreases by 0.8156932.
The log odds of loan approval for Hispanic applicants decreases by 0.9000102.
## Overall
## GDLIN1 17.126161
## OBRAT 3.305071
## BLACK1 3.396220
## HISPAN1 2.897795
## LOANPRC 3.313389
## MARRIED1 2.477753
## MALE1 0.229981
## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 293.3054 on 1 and 1961 df: p= < 0.000000000000000222
## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 10.9235 on 1 and 1961 df: p= 0.00096664
## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 11.53431 on 1 and 1961 df: p= 0.00069686
## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 8.397215 on 1 and 1961 df: p= 0.0037997
## Wald test for MALE
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 0.05289126 on 1 and 1961 df: p= 0.81813
## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 10.97855 on 1 and 1961 df: p= 0.00093849
## Wald test for MARRIED
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 6.13926 on 1 and 1961 df: p= 0.013305
## llh llhNull G2 McFadden r2ML
## -479.7016510 -737.7148785 516.0264551 0.3497465 0.2305470
## r2CU
## 0.4372079
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.34239 3.72139 -0.03410 -0.81143 -0.89733
## LOANPRC MARRIED1
## -0.01677 0.46093
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1962 Residual
## Null Deviance: 1475
## Residual Deviance: 959.5 AIC: 973.5
## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 294.1283 on 1 and 1962 df: p= < 0.000000000000000222
## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 10.93867 on 1 and 1962 df: p= 0.00095878
## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 11.47424 on 1 and 1962 df: p= 0.00071961
## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 8.358631 on 1 and 1962 df: p= 0.0038808
## Wald test for MARRIED
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 6.482227 on 1 and 1962 df: p= 0.010972
## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 10.92337 on 1 and 1962 df: p= 0.00096669
For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0340979.
For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0167734.
The log odds of loan approval for applicants that meet credit guidelines increase by 3.721387.
The log odds of loan approval for married applicants decreases by 0.4757419.
The log odds of loan approval for non married applicants decreases by NA.
The log odds of loan approval for Black applicants decreases by 0.8114263.
The log odds of loan approval for Hispanic applicants decreases by 0.8973309.
## 2.5 % 97.5 %
## (Intercept) 0.23664368 2.465735226
## GDLIN1 3.30547346 4.157682544
## OBRAT -0.05434377 -0.013920887
## BLACK1 -1.27292218 -0.332543498
## HISPAN1 -1.48462721 -0.264593691
## LOANPRC -0.02697832 -0.006937324
## MARRIED1 0.10487116 0.815796783
## 2.5 % 97.5 %
## (Intercept) 0.23158635 2.453187301
## GDLIN1 3.29609767 4.146676358
## OBRAT -0.05430447 -0.013891283
## BLACK1 -1.28092587 -0.341926697
## HISPAN1 -1.50565235 -0.289009441
## LOANPRC -0.02672039 -0.006826433
## MARRIED1 0.10609951 0.815760700
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1 LOANPRC
## 3.8281698 41.3216682 0.9664769 0.4442240 0.4076563 0.9833665
## MARRIED1
## 1.5855480
## OR 2.5 % 97.5 %
## (Intercept) 3.8281698 1.2669896 11.7721341
## GDLIN1 41.3216682 27.2614457 63.9232116
## OBRAT 0.9664769 0.9471065 0.9861756
## BLACK1 0.4442240 0.2800122 0.7170975
## HISPAN1 0.4076563 0.2265868 0.7675177
## LOANPRC 0.9833665 0.9733823 0.9930867
## MARRIED1 1.5855480 1.1105675 2.2609765
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.66805 3.69461 -0.03512 -0.81768 -0.85828
## LOANPRC
## -0.01659
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1963 Residual
## Null Deviance: 1475
## Residual Deviance: 965.9 AIC: 977.9
## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 294.1283 on 1 and 1962 df: p= < 0.000000000000000222
## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 10.93867 on 1 and 1962 df: p= 0.00095878
## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 11.47424 on 1 and 1962 df: p= 0.00071961
## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 8.358631 on 1 and 1962 df: p= 0.0038808
## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 10.92337 on 1 and 1962 df: p= 0.00096669
For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0351171.
For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0165852.
The log odds of loan approval for applicants that meet credit guidelines increases by 3.6946116.
The log odds of loan approval for Black applicants decreases by 0.8176845.
The log odds of loan approval for Hispanic applicants decreases by 0.8582767.
## 2.5 % 97.5 %
## (Intercept) 0.59360475 2.764561689
## GDLIN1 3.28231679 4.126731408
## OBRAT -0.05537654 -0.014888611
## BLACK1 -1.27852143 -0.339452086
## HISPAN1 -1.44328269 -0.227316096
## LOANPRC -0.02676923 -0.006824773
## 2.5 % 97.5 %
## (Intercept) 0.58607300 2.750024092
## GDLIN1 3.27321875 4.116004514
## OBRAT -0.05536176 -0.014872430
## BLACK1 -1.28654690 -0.348822144
## HISPAN1 -1.46462838 -0.251925037
## LOANPRC -0.02649064 -0.006679743
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1 LOANPRC
## 5.3018115 40.2299456 0.9654924 0.4414526 0.4238919 0.9835516
## OR 2.5 % 97.5 %
## (Intercept) 5.3018115 1.8105031 15.8720816
## GDLIN1 40.2299456 26.6374146 61.9750205
## OBRAT 0.9654924 0.9461288 0.9852217
## BLACK1 0.4414526 0.2784487 0.7121604
## HISPAN1 0.4238919 0.2361513 0.7966689
## LOANPRC 0.9835516 0.9735859 0.9931985
## Analysis of Deviance Table
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1961 959.40
## 2 1962 959.46 -1 -0.0531 0.81770
## 3 1963 965.87 -1 -6.4163 0.01131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Likelihood ratio test
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 8 -479.70
## 2 7 -479.73 -1 0.0531 0.81770
## 3 6 -482.94 -1 6.4163 0.01131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 0.566210 2.142459 -0.016400 -0.425865 -0.463475
## LOANPRC MARRIED1 MALE1
## -0.008409 0.237894 -0.033267
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1961 Residual
## Null Deviance: 1475
## Residual Deviance: 958.8 AIC: 974.8
## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 312.1492 on 1 and 1961 df: p= < 0.000000000000000222
## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 9.41885 on 1 and 1961 df: p= 0.0021771
## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 11.25188 on 1 and 1961 df: p= 0.00081057
## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 8.034928 on 1 and 1961 df: p= 0.0046354
## Wald test for MALE
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 0.0795587 on 1 and 1961 df: p= 0.77793
## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 10.54337 on 1 and 1961 df: p= 0.0011857
## Wald test for MARRIED
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 6.123722 on 1 and 1961 df: p= 0.013422
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = binomial(link = "probit"), data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 0.541687 2.143873 -0.016411 -0.422677 -0.461722
## LOANPRC MARRIED1
## -0.008386 0.228926
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1962 Residual
## Null Deviance: 1475
## Residual Deviance: 958.9 AIC: 972.9
## Overall
## GDLIN1 17.691026
## OBRAT 3.070619
## BLACK1 3.337594
## HISPAN1 2.825314
## LOANPRC 3.239942
## MARRIED1 2.530275
## llh llhNull G2 McFadden r2ML
## -479.4603569 -737.7148785 516.5090432 0.3500736 0.2307356
## r2CU
## 0.4375655
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = binomial(link = "probit"), data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 0.708006 2.135031 -0.017003 -0.426583 -0.438093
## LOANPRC
## -0.008356
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1963 Residual
## Null Deviance: 1475
## Residual Deviance: 965.3 AIC: 977.3
## Overall
## GDLIN1 17.692269
## OBRAT 3.183979
## BLACK1 3.379077
## HISPAN1 2.687345
## LOANPRC 3.247739
## llh llhNull G2 McFadden r2ML
## -482.6350057 -737.7148785 510.1597458 0.3457703 0.2282510
## r2CU
## 0.4328537
## Analysis of Deviance Table
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1961 958.84
## 2 1962 958.92 -1 -0.0799 0.77742
## 3 1963 965.27 -1 -6.3493 0.01174 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Likelihood ratio test
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 8 -479.42
## 2 7 -479.46 -1 0.0799 0.77742
## 3 6 -482.64 -1 6.3493 0.01174 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## GDLIN OBRAT BLACK HISPAN MARRIED LOANPRC
## 1 Does not meet guidelines 0 1 0 Not Married 77.06418
## 2 Does not meet guidelines 1 1 0 Not Married 77.06418
## 3 Does not meet guidelines 2 1 0 Not Married 77.06418
## 4 Does not meet guidelines 3 1 0 Not Married 77.06418
## 5 Does not meet guidelines 4 1 0 Not Married 77.06418
## 6 Does not meet guidelines 5 1 0 Not Married 77.06418
## fit se.fit residual.scale UL LL PredictedProb
## 1 -0.7616686 0.4664814 1 0.5380848 0.1576296 0.3182841
## 2 -0.7957664 0.4585300 1 0.5257154 0.1551869 0.3109318
## 3 -0.8298643 0.4506741 1 0.5133610 0.1527510 0.3036738
## 4 -0.8639622 0.4429189 1 0.5010397 0.1503213 0.2965122
## 5 -0.8980601 0.4352697 1 0.4887690 0.1478973 0.2894493
## 6 -0.9321579 0.4277323 1 0.4765665 0.1454785 0.2824871
## RACE
## 1 non-Hispanic Black
## 2 non-Hispanic Black
## 3 non-Hispanic Black
## 4 non-Hispanic Black
## 5 non-Hispanic Black
## 6 non-Hispanic Black